英文标题：
《Monotonicity of the collateralized debt obligations term structure model》
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作者：
Micha{\\l} Barski
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最新提交年份：
2015
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英文摘要：
The problem of existence of arbitrage free and monotone CDO term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates with the use of the Milian type result are formulated. Two state spaces are taken into account - of square integrable functions and a Sobolev space. For the first the regularity results concerning pointwise monotonicity are proven. Arbitrage free and monotone models are characterized in terms of the volatility of the model and characteristics of the driving L\\\'evy process.
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中文摘要：
研究了无套利单调CDO期限结构模型的存在性问题。利用Milian型结果，给出了相应的Heath-Jarrow-Morton-Musiela方程在$x$远期利率下的正性和单调性条件。考虑了两个状态空间——平方可积函数和Sobolev空间。首先证明了关于点态单调性的正则性结果。无套利和单调模型的特征是模型的波动性和驱动Lāevy过程的特征。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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